We discuss the error analysis for a moving-boundary system in two phases arising from modeling the penetration of a sharp carbonation front into unsaturated cement-based materials. The special feature of this problem is that the moving boundary is driven by a kinetic condition proportional to the rate of a fast carbonation reaction concentrated on the moving boundary. We prove a priori error es...

This paper deals with a theoretical mathematical analysis of one-dimensional solidification problem, in which kinetic undercooling is incorporated into the This temperature condition at the interface. A model problem with nonlinear kinetic law is considered. We prove a local result intimate for the uniqueness of solution of the corresponding free boundary problem.

Viscous fingering patterns that occur at the interface between two immiscible fluids of differing viscosities in a Hele-Shaw cell are normally studied mathematically via nonlinear moving boundary problem with single interface. Here we study more realistic model which involves doubly connected region viscous fluid bounded by interfaces. We simulate this numerically using level set method, suppor...

Level set methods for moving interface problems require efficient techniques for transforming an interface to a globally defined function whose zero set is the interface, such as the signed distance to the interface. This paper presents efficient algorithms for this “redistancing” problem. The algorithms use quadtrees and triangulation to compute global approximate signed distance functions. A ...

We determine the asymptotic behavior of the system of Cahn-Hillard/Euler's equations that control the dynamics inside the thin boundary layer separating two inviscid, incompressible, and nearly immiscible fluids. This model was proposed recently in order to replace the classical moving boundary model of two immiscible fluids, separated by the interface with the surface tension. We formally veri...

The Stefan problem is one of the best known parabolic two-phase free boundary problems. It is a simple model of phase transitions in liquid-solid systems. Let Ω⊂Rn denote a domain that contains a liquid and a solid separated by an interface Γ. As the melting or cooling take place the boundary moves and we are naturally led to a free boundary problem. The unknowns are the temperatures of the liq...

Interfacial flows close to a moving contact line are inherently multiscale. The shape of the interface and the flow at meso- and macroscopic scales inherit an apparent interface slope and a regularization length, both named after Voinov, from the microscopic inner region. Here, we solve the inner problem associated with the contact line motion for a volatile fluid at equilibrium with its vapor....

with the rise in the use of afm (atomic force microscope), we have witnessed a growing use of atomic microscope based nanorobots in the precise displacement of various particles. there are certain limitations to the application of nanorobots in the moving of nanoparticles. one of the most important of these limitations is the lack of an appropriate image feedback concurrent with the displaci...